Finite Group DatabasebetaFinite Group Databasebeta| order | 5100 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17×C25 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C17×C25 |
| unambiguous semidirect product | C3⋊(C4×C17×C25) |
| derived, Sylow | C3 ⋊ C4×C17×C25 |
| Hall | C3×C17×C25 ⋊ C4 |
| Hall | C3×C25 ⋊ C4×C17 |
| Hall | C3×C17 ⋊ C4×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17×C25 | D3 |
| commutator, hypocenter | C3 | C4×C17×C25 |
| Frattini | C2×C5 | C5×D3×C17 |
| Fitting | C2×C3×C17×C25 | C2 |
| socle | C2×C3×C5×C17 | C2×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C17×C25 | |
36 conjugacy classes of subgroups.
2550 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×C25×Dic9, C3×Dic3×C17×C25, C17×C25×C3⋊Dic3, … |
| maximal normal subgroup of | C3×Dic3×C17×C25, C7×Dic3×C17×C25 |
| maximal quotient of | C17×C25×Dic9, C3×Dic3×C17×C25, C17×C25×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5100, 5);